The 18-year-old needed to stop and reattach the shoe with about 550 metres to go, then roared to victory in eight minutes, 58.78 seconds.
Only Bahrain's Ruth Jebet, whose world record is 8:52.78, has run faster.
"It was difficult but I try my best," Chespol said. "I'm happy of course."
The world youth and under-20 champion improved her personal best by almost six seconds. She had run 9:05.70 three weeks ago in Doha.
Compatriot Beatrice Chepkoech claimed second in 9:00.70 with Jebet a trailing third almost three seconds adrift of Chepkoech.
Ethiopian Genzebe Dibaba ran away with the women's 5,000 metres but was well off her sister Tirunesh's world record, which she had hoped to break.
Dibaba, running solo for nearly half the race, finished in 14:25.22, far behind Tirunesh's 2008 record of 14:11.15.
"I'm happy that I won but I'm not happy about the time," Dibaba said through an interpreter. "The pace was real slow and I'm not happy with how we started.
"We lost time in the first 3,000 metres and it was hard to come back after that."
Kenyan Lilian Rengeruk took second in 14:36.80 with Dutch Sifan Hassan third in 14:41.24.
Rio Olympic silver medallist Brittney Reese delivered the first seven-metre leap of the outdoor season to win the long jump.
Reese, the London Olympic champion, hit 7.01 metres on her second attempt to outduel fellow American and Rio winner Tianna Bartoletta, who leaped 6.83 metres.
"I was really pleased," Reese said. "The goal was to come out and jump seven meters. I feel like I’m headed in the right direction."
The meeting continues on Saturday with British double Olympic champion Mo Farah running the last track race of his career in the United States when he faces a high-quality field in the 5,000 metres.
Farah, who trains in nearby Portland, will concentrate on the marathon after August's world championships in London.
(Editing by Amlan Chakraborty)
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